arXiv Open Access 2019

Continuous quivers of type A (I) Foundations

Kiyoshi Igusa Job D. Rock Gordana Todorov

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Abstrak

We generalize type $A$ quivers to continuous type $A$ quivers and prove initial results about pointwise finite-dimensional (pwf) representations. We classify the indecomosable pwf representations and provide a decomposition theorem, recovering results of Botnan and Crawley-Boevey. We also classify the indecomposable pwf projective representations. Finally, we prove that many of the properties of finite-dimensional type $A_n$ representations are present in finitely generated pwf representations. This is the self-contained foundational part of a series of works to study a generalization of continuous clusters categories and their relationship to other type $A$ cluster structures.

Topik & Kata Kunci

math.RT

Penulis (3)

Kiyoshi Igusa

Job D. Rock

Gordana Todorov

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APA MLA BibTeX

Igusa, K., Rock, J.D., Todorov, G. (2019). Continuous quivers of type A (I) Foundations. https://arxiv.org/abs/1909.10499

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Informasi Jurnal

Tahun Terbit: 2019
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓